US President Donald Trump today lashed out the appointment of a special counsel to probe allegations of his campaign's collusion with Russia into last year's general elections, calling it the single greatest "witch hunt" of a politician in American history.

The Justice Department named former FBI Director Robert Mueller as special counsel to investigate alleged Russian interference in the 2016 US election and possible collusion between Trump's campaign and Moscow.

The decision by deputy attorney general Rod Rosenstein to appoint Mueller, 72, as special counsel came following a week of turmoil for the White House after Trump fired FBI Director James Comey, who had been leading a federal probe into the matter.

Reacting to the appointment, Trump earlier said a thorough investigation will prove that no such collusion took place.

"As I have stated many times, a thorough investigation will confirm what we already know - there was no collusion between my campaign and any foreign entity. I look forward to this matter concluding quickly," Trump said in a statement.

"In the meantime, I will never stop fighting for the people and the issues that matter most to the future of our country," he had said.

However, Trump later lashed out at the appointment of the special counsel in a series of tweets.

"This is the single greatest witch hunt of a politician in American history!" Trump said in a tweet.

"With all of the illegal acts that took place in the Clinton campaign and the Obama administration, there was never a special councel appointed," Trump said in another tweet.

Earlier, the US was rocked by revelations that Comey wrote memos of his past meetings with Trump, including one at which the president apparently asked him to stop an investigation of former national security adviser Michael Flynn. The White House denied that account.

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